1. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 3-1 Round each number to the underlined place value. a. 89.63 b. 579,122 c. 0.83476 90600,0000.8348

2. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 (For help, go to Skills Handbook page 727.) Use the number 27.3865. Write the value of the given digit. 1.2 2.3 3.8 4.6 Check Skills You’ll Need 3-1

3. Solutions 1.27.3865; 2 tens2.27.3865; 3 tenths 3.27.3865; 8 hundredths4.27.3865; 6 thousandths Rounding and Estimating PRE-ALGEBRA LESSON 3-1 3-1

4. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 a. Round 8.7398 to the nearest tenth. 8.7398 tenths place less than 5 8.7 Round down to 7. 3-1

5. (continued) Rounding and Estimating PRE-ALGEBRA LESSON 3-1 b. Round 8.7398 to the nearest integer. 8.7398 nearest integer is ones place 5 or greater 9 Round up to 9. Quick Check 3-1

6. Estimate to find whether each answer is reasonable. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 a. Calculation +$ 59.98 $ 83.21 $115.67 $258.86 +$ 60 $ 80 $120 Estimate $260 The answer is close to the estimate. It is reasonable. 3-1

7. (continued) Rounding and Estimating PRE-ALGEBRA LESSON 3-1 b. Calculation –$ 39.34 $176.48 $147.14 Estimate –$ 40 $180 $140 The answer is not close to the estimate. It is not reasonable. Quick Check 3-1

8. Add the front-end digits. You are buying some fruit. The bananas cost $1.32, the apples cost $2.19, and the avocados cost $1.63. Use front-end estimation to estimate the total cost of the fruit. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 5.10= The total cost is about $5.10. + Estimate by rounding..60.20.30 1.10 Quick Check 3-1

9. Estimate the total electricity charge: March: $81.75; April: $79.56; May: $80.89. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 240= The total electricity charge is about $240.00. The values cluster around $80. 80 3 months 3 Quick Check 3-1

10. Round to the underlined place. 1.6.557 2.3.0448 Estimate. 3.$4.95 + $.89 4.4.589 + 5.098 + 5.179 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 about $6.00 6.63.04 about 15 3-1

11. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 3-2 Round to the nearest whole number and to the nearest tenth. a. 4.07 b. 0.708 c. 364.825 4, 4.1 1, 0.7 365, 364.8

12. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 (For help, go to Lesson 3-1.) Round to the nearest one. 1.145.89 2.199.27 3.101.06 4.28.45 Check Skills You’ll Need 3-2

13. Solutions nearest integer nearest integer 1. 145.892.199.27 5 or greater; round up to 6 less than 5; do not change 146 199 nearest integer nearest integer 3.101.064.28.45 less than 5; do not change less than 5; do not change 101 28 Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 3-2

14. Estimate 6.43 4.7. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Multiply.6 5 = 30 6.4364.75Round to the nearest integer. 6.43 4.7 30 Quick Check 3-2

15. Joshua bought 3 yd of fabric to make a flag. The fabric cost $5.35/yd. The clerk said his total was $14.95 before tax. Did the clerk make a mistake? Explain. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Multiply 5 times 3, the number of yards of fabric. 5 3 = 15 5.355Round to the nearest dollar. The sales clerk made a mistake. Since 5.35 > 5, the actual cost should be more than the estimate. The clerk should have charged Joshua more than $15.00 before tax. Quick Check 3-2

16. The cost to ship one yearbook is $3.12. The total cost for a shipment was $62.40. Estimate how many books were in the shipment. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 3.123Round the divisor. The shipment is made up of about 20 books. 62.4060 Round the dividend to a multiple of 3 that is close to 62.40. 60 ÷ 3 = 20Divide. Quick Check 3-2

17. Is 3.29 a reasonable quotient for 31.423 ÷ 5.94? Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Since 3.29 is not close to 5, it is not reasonable. 5.946Round the divisor. 31.42330 Round the dividend to a multiple of 6 that is close to 31.423. 30 ÷ 6 = 5Divide. Quick Check 3-2

18. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Estimate each product or quotient. 1.$4.78 ÷ 0.891 2.983.24 2.41 3.–5.89 ÷ (–2.7) 4.24.69 0.7 5.20.498 4.908 about 100 about $5about 2,000 about 2about 25 3-2

19. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 3-3 Order from greatest to least: 0.677, 0.855, 0.760, 0.078, 0.541 0.855, 0.760, 0.677, 0.541, 0.078

20. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 (For help, go Skills Handbook page 723.) Write the numbers from least to greatest. 1.8, 6, 4, 9, 3, 5, 6 2.72, 68, 69, 71, 72 3.112, 101, 98, 120, 101 4.3.74, 3, 3.7, 3.3, 37 Check Skills You’ll Need 3-3

21. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Solutions 1.3, 4, 5, 6, 6, 8, 92.68, 69, 71, 72, 72 3.98, 101, 101, 112, 1204.3, 3.3, 3.7, 3.74, 37 3-3

22. Six elementary students are participating in a one-week Readathon to raise money for a good cause. Use the graph. Find the (a) mean, (b) median, and (c) mode of the data if you leave out Latana’s pages. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 a. Mean: 40 + 45 + 48 + 50 + 50 5 = 233 5 = 46.6= The mean is 46.6. sum of data values number of data values 3-3

23. (continued) Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 b. Median: 40 45 48 50 50 Write the data in order. The median is the middle number, or 48. c. Mode: Find the data value that occurs most often. The mode is 50. Quick Check 3-3

24. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 a. $1.10 $1.25 $2.00 $2.10 $2.20 $3.50 No values are the same, so there is no mode. b. 1 3 4 6 7 7 8 9 10 12 12 13 How many modes, if any, does each have? Name them. c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape There is one mode. Both 7 and 12 appear more than the other data values. Cherry appears most often. Since they appear the same number of times, there are two modes. 3-3 Quick Check

25. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 a. Which data value is an outlier? Use the data: 7%, 4%, 10%, 33%, 11%, 12%. The data value 33% is an outlier. b. How does the outlier affect the mean? The outlier raises the mean by about 5.5 points. 12.8 – 7.3 = 5.5 It is an outlier because it is 21% away from the closest data value. Find the mean with the outlier. 77 6 12.8 Find the mean without the outlier. 44 6 7.3 3-3 Quick Check

26. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 a. the monthly amount of rain for a year Which measure of central tendency best describes each situation? Explain. since the average monthly amount of rain for a year is not likely to have an outlier, mean is the appropriate measure. Mean; b. most popular color of shirt Mode; When the data have no outliers, use the mean. When determining the most frequently chosen item, or when the data are not numerical, use the mode. since the data are not numerical, the mode is the appropriate measure. 3-3

27. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 c. times school buses arrive at school (continued) since one bus may have to travel much farther than other buses, the median is the appropriate measure. Median; When an outlier may significantly influence the mean, use the median. 3-3 Quick Check

28. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Which measure of central tendency best describes each situation? 1.numbers of legs on the animals in a zoo 2.favorite digits (from 0 to 9) of the students in a class 3.numbers of days-per-student that students are absent from school 4.test scores median mode mean 3-3

29. Using Formulas PRE-ALGEBRA LESSON 3-4 3-4 Evaluate each expression for r = 4, s = 6, t = 2. a. 4r b. 18 ÷ s + t c. (r + s) 2 165 20

30. Using Formulas PRE-ALGEBRA LESSON 3-4 (For help, go to Lesson 1-3.) Evaluate each expression for x = 3 and y = 4. 1.2x + 2y 2.2x + y 3.2(x + y) 4. x + y 2 Check Skills You’ll Need 3-4

31. Using Formulas PRE-ALGEBRA LESSON 3-4 Solutions 1.2x + 2y = 2(3) + 2(4)2.2x + y = 2(3) + (4) = 6 + 8 = 6 + 4 = 14 = 10 3.2(x + y) = 2(3 + 4)4. = = 2(7) = 14 x + y 2 3 + 4 2 = = 3.5 7272 3-4

32. Using Formulas PRE-ALGEBRA LESSON 3-4 Suppose you ride your bike 18 miles in 3 hours. Use the formula d = r t to find your average speed. d = r tWrite the formula. 18 = (r )(3)Substitute 18 for d and 3 for t. Divide each side by 3. 18 3 = 3r33r3 Simplify.6 = r Your average speed is 6 mi/h. Quick Check 3-4

33. Use the formula F = + 37, where n is the number of chirps a cricket makes in one minute, and F is the temperature in degrees Fahrenheit. Estimate the temperature when a cricket chirps 76 times in a minute. Using Formulas PRE-ALGEBRA LESSON 3-4 n4n4 The temperature is about 56°F. F = + 37 n4n4 Write the formula. F = + 37 76 4 Replace n with 76. F = 19 + 37Divide. F = 56Add. Quick Check 3-4

34. Find the perimeter of a rectangular tabletop with a length of 14.5 in. and width of 8.5 in. Use the formula for the perimeter of a rectangle, P = 2 + 2w. Using Formulas PRE-ALGEBRA LESSON 3-4 The perimeter of the tabletop is 46 in. P = 2 + 2wWrite the formula. P = 46Add. P = 2(14.5) + 2(8.5)Replace with 14.5 and w with 8.5. P = 29 + 17Multiply. Quick Check 3-4

35. Using Formulas PRE-ALGEBRA LESSON 3-4 Use the formula P = 4s to find the perimeter of a square with side s. 1. s = 5.6 m 2.s = 9.3 in. 3.Find the side of a square with a perimeter of 164 yd. 41 yd 22.4 m37.2 in. 3-4

36. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 3-5 Separate the digits 1 through 9 into three groups that have the same sum. 1, 5, 9; 2, 6, 7; 3, 4, 8

37. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 (For help, go to Skills Handbook page 730.) Simplify. 1.2.8 + 7.06 2.0.65 + 1.8 3.4.52 – 2.48 4.3.7 – 0.62 Check Skills You’ll Need 3-5

38. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solutions 1.2.802.0.65 + 7.06+ 1.80 9.862.45 3.4.524.3.70 – 2.48– 0.62 2.043.08 3-5

39. Solve 6.8 + p = –9.7. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 6.8 + p = –9.7 6.8 – 6.8 + p = –9.7 – 6.8Subtract 6.8 from each side. p = –16.5Simplify. Check6.8 + p = –9.7 6.8 + (–16.5) –9.7Replace p with –16.5. –9.7 = –9.7 Quick Check 3-5

40. Ping has a board that is 14.5 ft long. She saws off a piece that is 8.75 ft long. Use the diagram below to find the length of the piece that is left. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 The length of the piece that is left is 5.75 ft. x = 5.75Simplify. x + 8.75 – 8.75 = 14.5– 8.75 Subtract 8.75 from each side. x + 8.75 = 14.5 Quick Check 3-5

41. Solve –23.34 = q – 16.99. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 –23.34 = q – 16.99 –23.34 + 16.99 = q – 16.99 + 16.99Add 16.99 to each side. –6.35 = qSimplify. Quick Check 3-5

42. Alejandro wrote a check for $49.98. His new account balance is $169.45. What was his previous balance? Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Alejandro had $219.43 in his account before he wrote the check. Simplify.p = 219.43 Add 49.98 to each side.p – 49.98 + 49.98 = 169.45 + 49.98 p – 49.98 = 169.45 Equation p –$49.98= $169.45 Let p = previous balance. Words previous balance minus check is new balance Quick Check 3-5

43. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve each equation. 1.a + 10 = 7.9 2.–1.01 = c – 9 3.s – (–2.6) = 1.6 4.3.02 + d = 2.91 5.–23.7 = 13.3 + g – 37 – 2.17.99 – 1– 0.11 3-5

44. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 3-6 Lucinda buys 12 gal of gasoline at $1.95 per gallon. How much does the gas cost? $23.40

45. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 (For help, go to Skills Handbook page 765.) Find each product. 1.2.6(4.5) 2.3.2(0.15) 3.11.03(0.6) 4.8.003(0.6) Check Skills You’ll Need 3-6

46. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solutions 1.2.62.0.15  4.5  3.2 13030 + 1040+ 450 11.70= 11.70.480= 0.48 3.11.034.8.003  0.6 6.6184.8018 3-6

47. Solve –6.4 = 0.8b. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 –6.4 = 0.8b –6.4 0.8 0.8b 0.8 = Divide each side by 0.8. –8 = bSimplify. Check–6.4 = 0.8b –6.4 0.8(–8)Replace b with –8. –6.4 = –6.4 Quick Check 3-6

48. Every day the school cafeteria uses about 85.8 gallons of milk. About how many days will it take for the cafeteria to use the 250 gallons in the refrigerator? Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Let x = number of days. number of days Words timesis250 gallons daily milk consumption Equation=85.8 x250 3-6

49. (continued) Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 85.8x = 250 The school will take about 3 days to use 250 gallons of milk. x = 2.914...Simplify. x3Round to the nearest whole number. 85.8x 85.8 = 250 85.8 Divide each side by 85.8. Quick Check 3-6

50. Solve –37.5 =. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 c –1.2 –37.5 = c –1.2 Multiply each side by –1.2.–37.5(–1.2) = (–1.2) c –1.2 45 = cSimplify. Quick Check 3-6

51. A little league player was at bat 15 times and had a batting average of 0.133 (rounded to the nearest thousandth). The batting average formula is a =, where a is the batting average, h is the number of hits, and n is the number of times at bat. Use the formula to find the number of hits she made. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 hnhn a = hnhn 0.133 = h 15 Replace a with 0.133 and n with 15. 3-6

52. (continued) Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 0.133(15) = (15) h 15 Multiply each side by 15. Simplify. 1.995 = h 2 hSince h (hits) represents an integer, round to the nearest integer. The little league player made 2 hits. Quick Check 3-6

53. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solve each equation. 1.9b = –30.6 2.–10.8 = 3.2.45 = –0.7k 4. = 240 5.y ÷ (–0.3) = 146.7 – 44.01 –3.427 p –2.5 –3.5 t 3.7 888 3-6

54. Using the Metric System PRE-ALGEBRA LESSON 3-7 3-7 Use mental math to find each product or quotient. a. 8.75 × 100 b. 9.6 × 100 c. 4.6 ÷ 10 d. 0.94 × 100 e. 4.06 ÷ 100 875 960 0.46 94 0.0406

55. Using the Metric System PRE-ALGEBRA LESSON 3-7 (For help, go to Skills Handbook page 734.) Find each product or quotient. 1.5  100 2.14.06 ÷ 1,000 3.0.294  104.0.9 ÷ 100 Check Skills You’ll Need 3-7

56. Using the Metric System PRE-ALGEBRA LESSON 3-7 Solutions 1.5 1002.14.06 ÷ 1000 Move the decimal point 2 places to the right. 500.3 places to the left. 0.01406 5 100 = 500 14.06 ÷ 1000 = 0.01406 3.0.294 104.0.9 ÷ 100Move the decimal point 1 place to the right. 02.942 places to the left. 0.009 0.294 10 = 2.94 0.9 ÷ 100 = 0.009 3-7

57. Choose an appropriate metric unit. Explain your choice. Using the Metric System PRE-ALGEBRA LESSON 3-7 a. the width of a textbook b. the mass of a pair of glasses c. the capacity of a thimble Milliliter; a thimble will hold only a small amount of water. Gram; glasses have about the same mass as many paperclips, but less than this textbook. Centimeter; the width of a textbook is about two hands, or ten thumb widths, wide. Quick Check 3-7

58. Choose a reasonable estimate. Explain your choice. Using the Metric System PRE-ALGEBRA LESSON 3-7 a. capacity of a drinking glass: 500 L or 500 mL b. length of a hair clip: 5 m or 5 cm c. mass of a pair of hiking boots: 1 kg or 1 g 1 kg; the mass is about one half the mass of your math book. 5 cm; the length of a hair clip would be about 5 widths of a thumbnail. 500 mL; a drinking glass holds less than a quart of milk. Quick Check 3-7

59. Complete each statement. Using the Metric System PRE-ALGEBRA LESSON 3-7 a. 7,603 mL = L 7,603 ÷ 1,000 = 7.603To convert from milliliters to liters, divide by 1,000. 7,603 mL = 7.603 L 4.57 m = 457 cm To convert meters to centimeters, multiply by 100. 4.57  100 = 457 cm b. 4.57 m = cm Quick Check 3-7

60. A blue whale caught in 1931 was about 2,900 cm long. What was its length in meters? Using the Metric System PRE-ALGEBRA LESSON 3-7 Words centimeters per meter length in centimeters ÷ length in meters = 2,900Equation 10029 ÷= The whale was about 29 m long. Quick Check 3-7

61. PRE-ALGEBRA LESSON 3-7 Write the metric unit that makes each statement true. 1.23 kg = 23,000 2.970 cm = 9.7 Complete each statement. 3. g = 42 mg 4. km = 5,000 m gm 0.0425 Using the Metric System 3-7

62. PRE-ALGEBRA LESSON 3-8 Problem Solving Strategy: Act It Out 3-8 Describe the pattern. Then give the next three terms. 3, 6, 12, 24, 48,... Starting with 3, each number is two times the number before it: 96, 192, 384.

63. PRE-ALGEBRA LESSON 3-8 (For help, go to Lesson 1-7.) Write a rule for each number pattern. Find the next three numbers in the pattern. 1.0, 6, 12, 18,… 2.–18, –9, 0, 9,… 3.0, 2, 1, 3, 2, 4, 3,…4.7, 6, 8, 7, 9, 8, 10,… Problem Solving Strategy: Act It Out Check Skills You’ll Need 3-8

64. PRE-ALGEBRA LESSON 3-8 Problem Solving Strategy: Act It Out Solutions 1.0, 6, 12, 18,… Start with 0 and add 6 repeatedly. 0,6,12,18,24,30,36 +6+6+6+6+6+6 2.–18, –9, 0, 9,… Start with –18 and add 9 repeatedly. –18,–9,0,9,18,27,36 +9+9+9+9+9+9 3-8

65. PRE-ALGEBRA LESSON 3-8 Problem Solving Strategy: Act It Out 3.0, 2, 1, 3, 2, 4, 3,… Start with 0. Alternately add 2 and subtract 1. 0, 2, 1, 3,2,4,3,5,4,6 +2–1+2–1+2–1+2–1+2 Solutions (continued) 4.7, 6, 8, 7, 9, 8, 10,... Start with 7. Alternately subtract 1 and add 2. 7, 6, 8, 7, 9, 8,10, 9, 11, 10 –1+2–1+2–1+2–1+2–1 3-8

66. Marta gives her sister one penny on the first day of October, two pennies on the second day, and four pennies on the third day. She continues to double the number of pennies each day. On what date will Marta give her sister $10.24 in pennies? Problem Solving Strategy: Act It Out PRE-ALGEBRA LESSON 3-8 1 2 2 2 = 4 4 2 = 8 8 2 = 16 16 2 = 32 Number of pennies Days after the first 012345012345 Amount $0.01 $0.02 $0.04 $0.08 $0.16 $0.32 3-8

67. (continued) Problem Solving Strategy: Act It Out PRE-ALGEBRA LESSON 3-8 2 2 2 2 2 2 2 2 2 2 = 1024 You can tell from the pattern in the chart that you just need to count the number of 2’s multiplied until you reach 1,024, which is $10.24 in pennies. Marta will give her sister $10.24 in pennies on October 11. 10 twos = 10 days after the first penny is given Quick Check 3-8

68. PRE-ALGEBRA LESSON 3-8 Solve using any strategy. 1.On Monday, Jon reads page 45 of his book and continues to read until he finishes page 89. How many page does he read on Monday? 2.Marion put one penny in a bank. Each day after that she put in the bank double the number of pennies from the previous day until the bank was full. If the bank was full on the 8th day, when was the bank only half-full? 89 – 45 + 1, or 45 pages 7th day Problem Solving Strategy: Act It Out 3-8